Mathematics textbooks for elementary teachers as a resource for teacher learning: The case of multiplication of integers.

Despite broad concern about the mathematics knowledge of elementary teachers and evidence that textbooks influence the mathematics they are taught, little is known about the content of books used in their mathematics courses. Research efforts have been limited by the lack of shared guidelines about what the texts should convey and the lack of analytic techniques applicable to texts for future teachers, who need new understanding of the mathematics they studied as schoolchildren. This dissertation introduces a method for analyzing the content of these texts. The method is based on construction of a content map that functions as an analytic tool, showing what could be in the texts according to comprehensive review of the literature for the focal topic multiplication of integers and what should be in the texts according to policy documents. The map is used to compare what could and should be in the texts with what is in them. The content map method thus offers a way to uncover and characterize different ways mathematics is developed by authors, facilitating useful comparisons that can help improve teachers' opportunities to learn mathematics. Multiplication of integers was used to develop and test the method because of the wide variation in how this challenging topic can be developed. However, although one mathematics topic was used for the dissertation, the method can be used with other topics. The primary finding about the method is it produced a useful representation for analyzing the content of mathematics books designed for teaching teachers. For multiplication of integers in particular, the dissertation contributes a bibliography and a detailed inventory of the mathematical ideas. The primary finding about the textbooks themselves is that although all authors emphasize understanding of calculation procedures and principles used for multiplication of integers, opportunities to learn more about multiplication of integers varies by text. Some knowledge suggested as important within the literature receives only sporadic treatment in or is missing from the books.PhDEducationElementary educationMathematics educationTeacher educationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/127167/2/3429490.pd